期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2017
卷号：79
期号：2
页码：201-207
DOI：10.1007/s13171-017-0113-7
语种：English
出版社：Indian Statistical Institute
摘要：Sara van de Geer and Martin Wainwright combine astute convexity arguments and concentration inequalities for suprema of empirical processes to establish generic concentration inequalities for excess penalized risk. This note discusses possible refinements and extensions. In the Gaussian sequence model, concentration of reconstruction error is likely to be improvable and might depend on the effective sparsity of the typical penalized estimator. In the general setting, concentration of excess penalized risk should be complemented by concentration of empirical excess penalized risk. Recent results on penalized least-square estimation pave the way to such a extensions.
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